Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(1 - x\right) - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (- 1.0 x) y))

C

double code(double x, double y) {
	return (1.0 - x) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) - y
end function

Java

public static double code(double x, double y) {
	return (1.0 - x) - y;
}

Python

def code(x, y):
	return (1.0 - x) - y

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) - y;
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (- 1.0 x) y))

C

double code(double x, double y) {
	return (1.0 - x) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) - y
end function

Java

public static double code(double x, double y) {
	return (1.0 - x) - y;
}

Python

def code(x, y):
	return (1.0 - x) - y

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) - y;
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (- 1.0 x) y))

C

double code(double x, double y) {
	return (1.0 - x) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) - y
end function

Java

public static double code(double x, double y) {
	return (1.0 - x) - y;
}

Python

def code(x, y):
	return (1.0 - x) - y

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) - y;
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(1 - x\right) - y \]

2. Final simplification 100.0%

   \[\leadsto \left(1 - x\right) - y \]

Alternative 2: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1280000000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-83}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1280000000000.0)
   (- x)
   (if (<= x -3e-83) (- y) (if (<= x -5.2e-293) 1.0 (- y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1280000000000.0) {
		tmp = -x;
	} else if (x <= -3e-83) {
		tmp = -y;
	} else if (x <= -5.2e-293) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1280000000000.0d0)) then
        tmp = -x
    else if (x <= (-3d-83)) then
        tmp = -y
    else if (x <= (-5.2d-293)) then
        tmp = 1.0d0
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1280000000000.0) {
		tmp = -x;
	} else if (x <= -3e-83) {
		tmp = -y;
	} else if (x <= -5.2e-293) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1280000000000.0:
		tmp = -x
	elif x <= -3e-83:
		tmp = -y
	elif x <= -5.2e-293:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1280000000000.0)
		tmp = Float64(-x);
	elseif (x <= -3e-83)
		tmp = Float64(-y);
	elseif (x <= -5.2e-293)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1280000000000.0)
		tmp = -x;
	elseif (x <= -3e-83)
		tmp = -y;
	elseif (x <= -5.2e-293)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1280000000000.0], (-x), If[LessEqual[x, -3e-83], (-y), If[LessEqual[x, -5.2e-293], 1.0, (-y)]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.28e12

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 74.6%

         \[\leadsto \color{blue}{-x} \]

   4. Simplified 74.6%

      \[\leadsto \color{blue}{-x} \]

   if -1.28e12 < x < -3.0000000000000001e-83 or -5.1999999999999996e-293 < x

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around inf 47.0%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   3. Step-by-step derivation

      1. neg-mul-1 47.0%

         \[\leadsto \color{blue}{-y} \]

   4. Simplified 47.0%

      \[\leadsto \color{blue}{-y} \]

   if -3.0000000000000001e-83 < x < -5.1999999999999996e-293

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

         \[\leadsto \color{blue}{1 - \left(x + y\right)} \]

      2. flip-- 80.6%

         \[\leadsto \color{blue}{\frac{1 \cdot 1 - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)}} \]

      3. metadata-eval 80.6%

         \[\leadsto \frac{\color{blue}{1} - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)} \]

   3. Applied egg-rr 80.6%

      \[\leadsto \color{blue}{\frac{1 - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)}} \]
   4. Step-by-step derivation

      1. +-commutative 80.6%

         \[\leadsto \frac{1 - \color{blue}{\left(y + x\right)} \cdot \left(x + y\right)}{1 + \left(x + y\right)} \]

      2. +-commutative 80.6%

         \[\leadsto \frac{1 - \left(y + x\right) \cdot \color{blue}{\left(y + x\right)}}{1 + \left(x + y\right)} \]

      3. associate-+r+ 80.6%

         \[\leadsto \frac{1 - \left(y + x\right) \cdot \left(y + x\right)}{\color{blue}{\left(1 + x\right) + y}} \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{\frac{1 - \left(y + x\right) \cdot \left(y + x\right)}{\left(1 + x\right) + y}} \]

   6. Taylor expanded in y around 0 62.9%

      \[\leadsto \color{blue}{\frac{1 - {x}^{2}}{1 + x}} \]
   7. Step-by-step derivation

      1. unpow2 62.9%

         \[\leadsto \frac{1 - \color{blue}{x \cdot x}}{1 + x} \]

   8. Simplified 62.9%

      \[\leadsto \color{blue}{\frac{1 - x \cdot x}{1 + x}} \]

   9. Taylor expanded in x around 0 62.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1280000000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-83}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - x \leq 1.5:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= (- 1.0 x) 1.5) (- 1.0 y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= 1.5) {
		tmp = 1.0 - y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((1.0d0 - x) <= 1.5d0) then
        tmp = 1.0d0 - y
    else
        tmp = 1.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= 1.5) {
		tmp = 1.0 - y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (1.0 - x) <= 1.5:
		tmp = 1.0 - y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(1.0 - x) <= 1.5)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(1.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((1.0 - x) <= 1.5)
		tmp = 1.0 - y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(1.0 - x), $MachinePrecision], 1.5], N[(1.0 - y), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 x) < 1.5

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in x around 0 78.0%

      \[\leadsto \color{blue}{1 - y} \]

   if 1.5 < (-.f64 1 x)

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around 0 73.1%

      \[\leadsto \color{blue}{1 - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x \leq 1.5:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]

Alternative 4: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2200000000:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2200000000.0) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2200000000.0) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2200000000.0d0) then
        tmp = 1.0d0 - x
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2200000000.0) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2200000000.0:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2200000000.0)
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2200000000.0)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2200000000.0], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.2e9

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around 0 72.5%

      \[\leadsto \color{blue}{1 - x} \]

   if 2.2e9 < y

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around inf 75.7%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   3. Step-by-step derivation

      1. neg-mul-1 75.7%

         \[\leadsto \color{blue}{-y} \]

   4. Simplified 75.7%

      \[\leadsto \color{blue}{-y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2200000000:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5: 43.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1.0) (- x) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = -x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = -x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = -x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = -x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(-x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = -x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], (-x), 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in x around inf 72.5%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 72.5%

         \[\leadsto \color{blue}{-x} \]

   4. Simplified 72.5%

      \[\leadsto \color{blue}{-x} \]

   if -1 < x

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

         \[\leadsto \color{blue}{1 - \left(x + y\right)} \]

      2. flip-- 67.0%

         \[\leadsto \color{blue}{\frac{1 \cdot 1 - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)}} \]

      3. metadata-eval 67.0%

         \[\leadsto \frac{\color{blue}{1} - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)} \]

   3. Applied egg-rr 67.0%

      \[\leadsto \color{blue}{\frac{1 - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)}} \]
   4. Step-by-step derivation

      1. +-commutative 67.0%

         \[\leadsto \frac{1 - \color{blue}{\left(y + x\right)} \cdot \left(x + y\right)}{1 + \left(x + y\right)} \]

      2. +-commutative 67.0%

         \[\leadsto \frac{1 - \left(y + x\right) \cdot \color{blue}{\left(y + x\right)}}{1 + \left(x + y\right)} \]

      3. associate-+r+ 67.0%

         \[\leadsto \frac{1 - \left(y + x\right) \cdot \left(y + x\right)}{\color{blue}{\left(1 + x\right) + y}} \]

   5. Simplified 67.0%

      \[\leadsto \color{blue}{\frac{1 - \left(y + x\right) \cdot \left(y + x\right)}{\left(1 + x\right) + y}} \]

   6. Taylor expanded in y around 0 48.0%

      \[\leadsto \color{blue}{\frac{1 - {x}^{2}}{1 + x}} \]
   7. Step-by-step derivation

      1. unpow2 48.0%

         \[\leadsto \frac{1 - \color{blue}{x \cdot x}}{1 + x} \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{\frac{1 - x \cdot x}{1 + x}} \]

   9. Taylor expanded in x around 0 35.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 26.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[\left(1 - x\right) - y \]
2. Step-by-step derivation

   1. associate--l- 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]

   2. flip-- 61.1%

      \[\leadsto \color{blue}{\frac{1 \cdot 1 - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)}} \]

   3. metadata-eval 61.1%

      \[\leadsto \frac{\color{blue}{1} - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)} \]

3. Applied egg-rr 61.1%

   \[\leadsto \color{blue}{\frac{1 - \left(x + y\right) \cdot \left(x + y\right)}{1 + \left(x + y\right)}} \]
4. Step-by-step derivation

   1. +-commutative 61.1%

      \[\leadsto \frac{1 - \color{blue}{\left(y + x\right)} \cdot \left(x + y\right)}{1 + \left(x + y\right)} \]

   2. +-commutative 61.1%

      \[\leadsto \frac{1 - \left(y + x\right) \cdot \color{blue}{\left(y + x\right)}}{1 + \left(x + y\right)} \]

   3. associate-+r+ 61.1%

      \[\leadsto \frac{1 - \left(y + x\right) \cdot \left(y + x\right)}{\color{blue}{\left(1 + x\right) + y}} \]

5. Simplified 61.1%

   \[\leadsto \color{blue}{\frac{1 - \left(y + x\right) \cdot \left(y + x\right)}{\left(1 + x\right) + y}} \]

6. Taylor expanded in y around 0 45.1%

   \[\leadsto \color{blue}{\frac{1 - {x}^{2}}{1 + x}} \]
7. Step-by-step derivation

   1. unpow2 45.1%

      \[\leadsto \frac{1 - \color{blue}{x \cdot x}}{1 + x} \]

8. Simplified 45.1%

   \[\leadsto \color{blue}{\frac{1 - x \cdot x}{1 + x}} \]

9. Taylor expanded in x around 0 27.0%

   \[\leadsto \color{blue}{1} \]

10. Final simplification 27.0%

    \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))